D: The Infinite Square Roots of -1
p. 229-235
Résumé
We present D, a synbol that can be used in the universal alphabet that provides a computational path to the nilpotent Dirac equation (Diaz & Rowlands, 2004) and which results in a tractable computer representation of the infinite square roots of -1. We outline how the representation is derived, the properties of the representation, and how the form can be used. Think of D as an infinite table of 1's in any representation e.g. binary or hexadecimal. Any specified column Di of the table has the property that when multiplied with a row Di, the result is a representation of -1. Di multiplied with Dj anticommutes as - (Dj*Di) and produces Dk in a way identical to Hamilton's quaternion i, j, and k. With an infinite and uniquely identifiable set of such triad forms D can be considered both a symbol and because of this behaviour, an alphabet.
Texte
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Référence papier
Bernard M. Diaz et Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS, 19 | 2006, 229-235.
Référence électronique
Bernard M. Diaz et Peter Rowlands, « D: The Infinite Square Roots of -1 », CASYS [En ligne], 19 | 2006, mis en ligne le 29 August 2024, consulté le 20 September 2024. URL : http://popups.lib.uliege.be/1373-5411/index.php?id=2586
Auteurs
Bernard M. Diaz
Department of Computer Science
The University of Liverpool
Peach Street, Liverpool, UK, L69 7ZF
Peter Rowlands
Science Communication Unit, Department of Physics
The University of Liverpool
Peach Street, Liverpool, UK, L69 7ZF